Write a value of `int(sec^2x)/((5+tanx)^4)\ dx`

Explanation

Solution:

Let `\t=5+\tan \x \Rightarrow \dt=\sec ^2 \{xdx}`

I=`\int \frac{\sec ^{2} x d x}{(5+\tan x)^4}`

=`\int \frac{d t}{t^{4}}`

=`\int t^{-4} d t`

=`\frac{t^{-4+1}}{-4+1}+c `

=`\frac{t^{-3}}{-3}+c`

=`\frac{-1}{3 t^{3}}+c` where c is the constant of integration.